In January, US President Trump and Turnbull clashed over the agreement that strained ties between the countries.

Mike Pence waves as he gets into his car after arriving in Sydney on Friday

US Vice President Mike Pence has said America will honour a refugee resettlement deal with Australia that Donald Trump once described as ‘dumb’.

Pence told reporters that he had reassured Australian Prime Minister Malcolm Turnbull that the US would hold up its share of the agreement struck by the Obama administration, even if the US did not ‘admire’ the deal.

In January, US President Trump and Turnbull clashed over the agreement that strained ties between the countries.

Under the deal, the US would take up to 1,250 refugees that Australia houses in detention camps on the Pacific island nations of Nauru and Papua New Guinea.

Pence, in Australia to talk about the state of the US-Australia alliance and lay out the new administration's priorities for the region, met Turnbull and senior ministers in Sydney during his 10-day, four-country trip to the Pacific Rim.

"I bring greetings this morning from the President of the United States," Pence told Turnbull ahead of their meeting.

"I spoke to him first thing and he wanted me to pass along his very best regards to you. And the President wanted me to - early in this administration - to reaffirm the strong and historical alliance between the United States and Australia," the Vice President said.

Pence's visit Down Under is widely viewed as an effort to smooth relations with Australia in the wake of the highly-publicised argument between Turnbull and Trump.

After taking office, Trump was infuriated to learn that the previous Obama administration had agreed to a refugee resettlement deal with Australia where America would take up to 1,250 refugees that Australia houses in detention camps on the Pacific island nations of Nauru and Papua New Guinea.

Trump's anger led to a tense phone call with Turnbull in January and an angry tweet in which the president dubbed the deal ‘dumb’. The fall-out has strained the typically cosy alliance between the US and Australia.

A majority of Australians view Trump unfavourably and some critics of the president have urged Australia to distance itself from the US in favour of stronger ties with China.

Turnbull has resisted pressure to choose between the two countries, both of which are considered vital allies; the US is Australia's most important security partner, while China is its most important trading partner.

The affection Australia and the US usually share for each other is rooted in decades of co-operation on defence, intelligence and trade.

Australia has fought alongside the US in every major conflict since the First World War, and is one of the largest contributors to the US-led military campaign in Iraq and Syria.

The country is also part of the Five Eyes intelligence-sharing programme with the US, Canada, Britain and New Zealand.

Earlier, Pence met Australia's Governor General Peter Cosgrove, who said that the relationship between the two countries was as strong as it was since ‘the first time we saw each other on the battlefield in 1919’.

Cosgrove said that the alliance started an ‘unbreakable relationship’, telling Pence, "We've been with you every step of the way."

Pence was also meeting Foreign Minister Julie Bishop and the leader of the opposition party, Bill Shorten. On Sunday, he will tour Sydney's Opera House and visit a zoo.